Have good credit is very important. It shows that you are financially responsible. But in New York, there are many people with undocumented incomes. So a number of ways of dealing with this have become commonplace.
1) Gather your paperwork to show that you are not living week to week. This means the most recent monthly statement from your bank and recent statements from your savings account or brokerage accounts, if you have any. You want to show that you are not living on your last dime.
2) Offer, up front, to prepay as much rent as you possibly can. Don't wait for the landlord to ask you, because they won't. Just offer it. If you remove the risk for a landlord, you'll get the apartment. If you prepaid for an entire year, there is no risk to the landlord, so no reason to deny you the apartment. If you can't offer a year's rent, then offer 6 month's of rent. If you can't do that, offer 3 month's of rent.
3) Offer to give the landlord additional security. Again, anything that lowers the risk to the landlord helps you to rent.
4) If you're renting with a monthly rent of $1,500 or greater, get pre-approved by a corporate guarantor like Insurent.com. It will cost you about a month's rent, but it will go a long way to getting you an apartment.
5) Have a financially strong friend or family member be your guarantor.
RentDirectNewYork.com has an excellent renter's guide that talks about each of these strategies and more. You can find it here: http://www.rent-direct.com/rentingguide/Welcome.html
Good luck in renting.